The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  1  1  1  1  1  1  1  1  1  0  1  2  1  1  2  1  2  1  1  4  0  1  8  2  1  2  1  1  2  0  8  1  0  1  1  1 12  1
 0  2  0  6  4  6 12  2 14  8  6  0  4 10  4  2  0 14 14  4 12  6 12 10  8 10  0 10  6  4  2  4  6  4  2  2  8  0  0  2 14  4  2  6 12  4  6  8  2  0  2 12  0 12  2  4 10 10  2  8 14  2 12  6 10  8  0  4  2  2  8  2  4 14 10 12  4 14  2  8  0  4  0  6  2  2  4
 0  0 12  0  4  8  0  0  4  0  4  4  4  4  8 12  0  8 12  8  4  0  4 12  8  8  4  8 12 12  4  8  8  4  4  8  8  8 12  4  8  8 12  0  4 12 12  4  4  8  0  0  8  4  8  0  0  4  8  4  0  0  4 12  0 12  4  8 12 12  0 12  0  4  8 12 12  0  4  4  0  4 12  4  8  4 12
 0  0  0 12  0  0  8 12  0  4  4  4  4  8 12 12  8 12  4  4  8  0 12  8 12  0 12  4  0  8  4  8  8  0  0 12  0  0  0 12 12 12  0  8 12  4 12  8  4 12 12  8  4  8  0 12  8  0  8 12  4  0  4 12  4  8  8  0  0 12 12  8 12  0  0 12  0 12  4 12  4  8  8  0 12  8 12
 0  0  0  0  8  8  8  8  0  0  8  0  8  8  8  0  0  0  8  8  8  8  8  8  0  0  0  8  0  0  0  8  0  0  8  0  0  8  8  8  8  0  0  8  0  8  0  8  8  8  0  0  0  0  8  8  0  0  8  8  0  8  0  0  8  8  0  0  8  8  0  0  0  8  0  0  8  8  0  8  8  0  0  8  8  0  8

generates a code of length 87 over Z16 who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+196x^81+68x^82+286x^83+255x^84+510x^85+471x^86+720x^87+443x^88+444x^89+227x^90+160x^91+33x^92+158x^93+23x^94+32x^95+3x^96+30x^97+9x^98+18x^99+4x^101+2x^102+2x^105+1x^144

The gray image is a code over GF(2) with n=696, k=12 and d=324.
This code was found by Heurico 1.16 in 11.6 seconds.